Plotting Frequency Characteristics of a Second-Order System with Different Damping Ratios Using MATLAB

First, write out the fractional expression of the second-order system, determine the frequency range to be plotted, and then use the bode function to plot the frequency characteristic curves of the system for different damping values.

% Plotting frequency characteristics for different damping ratios

wn1=10;

zeta1=0.2:0.1:1.2;

w1=logspace(-1,2,100);

num1=wn1*wn1;

figure(1);

for k1=zeta1

den1=[1.0 2*k1*wn1 wn1*wn1 ];

[mag1, pha1,w2]=bode(num1,den1,w1);

subplot(211);

semilogx(w2,mag1);

hold on;

subplot(212);

semilogx(w2,pha1);

hold on;

end

subplot(211);

grid on; grid; grid;

title(‘Frequency Characteristics’);

xlabel(‘rad/s’);

ylabel(‘gain(dB)’);

subplot(212);

grid on; grid; grid;

title(‘Phase Characteristics’);

xlabel(‘rad/s’);

ylabel(‘degree(°)’);